Settlement will allow Western Digital to take part in investment rounds for Toshiba’s memory-manufacturing facilities

TOKYO—A battle of multibillion-dollar investments in the memory-chip business is set to accelerate in 2018 after partners Toshiba Corp. and Western Digital Corp. patched up their differences to take on market leader Samsung Electronics Co.

The semiconductors known as NAND flash memory chips are taking a growing role in many of today’s devices including smartphones, game machines and data servers.